Statistical inference of adaptive type II progressive hybrid censored data with dependent competing risks under...

Area of Science:

• Statistics
• Reliability Engineering
• Survival Analysis

Background:

• Complex systems often exhibit dependent failure mechanisms.
• Progressive hybrid censoring with partial failure information presents significant analytical challenges.
• Accurate statistical inference is crucial for system reliability and maintenance.

Purpose of the Study:

• To develop and compare statistical inference methods for adaptive type II progressive hybrid censored data under dependent competing risks.
• To establish both frequentist (maximum likelihood) and Bayesian estimation approaches for analyzing such complex data.
• To provide a practical framework for reliability testing and system analysis.

Main Methods:

• Marshall-Olkin bivariate exponential distribution for dependent competing risks.
• Maximum Likelihood Estimation (MLE) and Fisher Information-based confidence intervals.
• Bayesian estimation using Gamma-Dirichlet priors, Gibbs sampling, and Metropolis-Hastings algorithm.
• Monte Carlo simulations for performance evaluation and experimental design.
• Application to a practical reliability test case.

Main Results:

• Development of analytical methods for complex censored data with partial failure information.
• Comparison of the performance of MLE and Bayesian estimation techniques using various statistical indices.
• Validation of the proposed methods through extensive Monte Carlo simulations.
• Demonstration of the practical applicability and efficiency of the developed algorithm.

Conclusions:

• The proposed statistical framework effectively handles adaptive type II progressive hybrid censored data with competing risks.
• Both MLE and Bayesian methods provide viable approaches for reliability analysis, with performance varying based on data characteristics.
• The study offers a robust and applicable methodology for efficient reliability testing in complex systems.